The Ontology of Mathematical Programming — On the Limits of Logic and the Unexpressible
The Ontology of Mathematical Programming — On the Limits of Logic and the Unexpressible 1. Introduction — I Was Never Good at Calculations Since childhood, I’ve been deeply fascinated by mathematics. Not by problem-solving or calculations per se, but by the persistent question: “What is mathematics?” Why does 1 + 1 equal 2? Why is multiplication a repeated addition? Why do mathematical rules work the way they do? Even as I stumbled through standard education, I found myself drawn not to formulas, but to the nature and origin of mathematics itself. Over time, one realization emerged with clarity: Mathematics is a kind of programming language. Mathematics as an Executable Language 2. Mathematics as an Executable Language Mathematics is structured around symbols, rules, and logical order. Operators like + , × , = , ∈ , and ∑ resemble functions or control flow in code. Addition is repeated increase Multiplication is repeated addition Mathematical...